Elliptic curves with good reduction outside {2, 3, 5, 7, 11, 13}

Contents

• A table of rational elliptic curves (up to Q-isomorphism) with good reduction outside the first 6 primes. Each curve is given as a tuple (c4, c6), such that a Weierstrass model can be recovered as y^2 = x^3 - 27 c4 x - 54 c6.
• Mordell-Weil bases of Mordell curves that were used to compute the table.
• Code for computing the Mordel-Weil bases.
• The paper corresponding to this table.

Completeness of the table

The table is likely to be complete, however this is not proved yet. Proving completeness with our method should take about 50 more CPU years.

Authors

Alex J. Best, Benjamin Matschke.

Contributions

Edgar Costa:

• Analytic ranks and leading term of L-functions at 1/2 for all curves in the table.

License

Creative Commons BY-NC 4.0.